### All ACT Math Resources

## Example Questions

### Example Question #33 : Algebra

What is the slope of any line parallel to the line ?

**Possible Answers:**

**Correct answer:**

To answer this question, we must find the slope of a line parallel to the line .

When a line is parallel to another, they have the same slope. Therefore, if we find the slope of the line we are given, we will find the slope of any line that would be parallel to it.

To find the slope, we must put our equation into point-intercept form. Point-intercept form is displayed as the following:

, where is the slope and is where the line intercepts the -axis.

Note that to put a line into point-intercept form, you must solve for .

Therefore, we must solve for . So, for this data, we must first subtract both sides of the equation by :

This becomes:

Now we must divide each side by to get by itself:

This becomes:

Because is in our point-intercept form, the slope of our line is . Therefore, the slope of any line parallel to this line is also .

### Example Question #34 : Algebra

What is the slope of a line parallel to the line given by the equation:

?

**Possible Answers:**

**Correct answer:**

Parallel lines have the same slope. You find slope by using the general form of slope-intercept:

where represents the slope of the line and represents the -intercept.

For our equation we see that the

is

thus the anser is .

### Example Question #1 : How To Find The Slope Of Parallel Lines

What is the slope of a line parallel to the line defined by the equation:

**Possible Answers:**

**Correct answer:**

The slope of a line in slope-intercept form is given by the coefficient, in the equation:

. For two lines to be parallel, they have to have the same slope. Thus we see in our equation that and so a line that is parallel must also have a slope of

### Example Question #2 : How To Find The Slope Of Parallel Lines

Which of the following is the equation of a line parallel to the line .

**Possible Answers:**

**Correct answer:**

Parallel lines have equivalent slopes, so the correct answer is .

### Example Question #5 : How To Find Out If Lines Are Parallel

Which of the following lines is parallel to:

**Possible Answers:**

**Correct answer:**

First write the equation in slope intercept form. Add to both sides to get . Now divide both sides by to get . The slope of this line is , so any line that also has a slope of would be parallel to it. The correct answer is .

### Example Question #7 : How To Find Out If Lines Are Parallel

Which pair of linear equations represent parallel lines?

**Possible Answers:**

**Correct answer:**

Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "" spot in the linear equation ,

We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.

### Example Question #8 : How To Find Out If Lines Are Parallel

Which of the following equations represents a line that is parallel to the line represented by the equation ?

**Possible Answers:**

**Correct answer:**

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Because the given line has the slope of , the line parallel to it must also have the same slope.

### Example Question #1 : How To Find Out If Lines Are Parallel

Line passes through the points and . Line passes through the point and has a of . Are the two lines parallel? If so, what is their slope? If not, what are their slopes?

**Possible Answers:**

Yes, the lines are parallel with a slope of .

Yes, the lines are parallel with a slope of .

No, the lines are not parallel. Line has a slope of and line has a slope of .

No, the lines are not parallel. Line has a slope of and line has slope .

**Correct answer:**

Yes, the lines are parallel with a slope of .

Finding slope for these two lines is as easy as applying the slope formula to the points each line contains. We know that line contains points and , so we can apply our slope formula directly (pay attention to negative signs!)

.

Line contains point and, since the y-intercept is always on the vertical axis, . Thus:

The two lines have the same slope, , and are thus identical.

### Example Question #2 : How To Find Out If Lines Are Parallel

Line is described by the equation . Line passes through the points and . Are the two lines parallel? If so, what is their slope? If not, what are their slopes?

**Possible Answers:**

No, the lines are not parallel. Line has slope and line has slope .

Yes, the lines are parallel, and both lines have slope .

Yes, the lines are parallel, and both lines have slope .

No, the lines are not parallel. Line has slope and line has slope .

**Correct answer:**

No, the lines are not parallel. Line has slope and line has slope .

We are told at the beginning of this problem that line is described by . Since is our slope-intecept form, we can see that for this line. Since parallel lines have equal slopes, we must determine if line has a slope of .

Since we know that passes through points and , we can apply our slope formula:

Thus, the slope of line is 1. As the two lines do not have equal slopes, the lines are not parallel.